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Example Questions
Example Question #52 : Algebra
Quantity A:
Quantity B:
The two quantities are the same.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined.
Quantity A is greater.
To solve this problem, expand each function described by Quantities A and B:
Quantity A:
Quantity B:
Now note that Quantities A and B only differ in that Quantity A is greater by .
Since we are told that is greater than
and thus always positive, Quantity A must be greater than Quantity B for all possible values of
.
Example Question #11 : How To Find Out When An Equation Has No Solution
Quantity A:
Quantity B:
The two quantities are equal.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined.
Quantity A is greater.
Rather than manually finding common denominators and adding the fractions together, realize that
Since
Quantity A must be greater, and this can be seen without actually calculating its value.
Example Question #12 : How To Find Out When An Equation Has No Solution
Approximately, what was the percent growth of Beetleton's GDP from 2009 to 2010?
Percent growth is given as:
For Beetleton, this can be expressed as (in terms of billions of US dollars):
Example Question #51 : Gre Quantitative Reasoning
The sum of two integers is . The larger integer is
greater than the smaller integer. What is the positive difference between the two?
Let us write down what we are told in mathematical terms, designating the smaller integer as and the larger integer as
.
The sum of the two integers is :
And the larger integer is % greater than the smaller integer:
Writing the first equation in terms of gives:
Which allows us to find :
Thus, the positive difference between the two is found as
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